Fixed Point Theorems Over Extended ϕ,ψ-Metric Spaces and Applications in Differential Equations

The main aim of this research endeavor is to introduce a novel type of generalized metric space, termed an extended ϕ,ψ-metric space, to establish new fixed point results and employ them to prove the existence and uniqueness of solutions to first-order differential equations. To achieve this goal, w...

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Bibliographic Details
Published in:Journal of function spaces 2024-01, Vol.2024
Main Authors: Taleb, Mohammed M A, Al-Salehi, Saeed A A, Borkar, V C
Format: Article
Language:English
Subjects:
Differential equations
Fixed points (mathematics)
Inequality
Metric space
Theorems
Online Access:Get full text
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Summary:The main aim of this research endeavor is to introduce a novel type of generalized metric space, termed an extended ϕ,ψ-metric space, to establish new fixed point results and employ them to prove the existence and uniqueness of solutions to first-order differential equations. To achieve this goal, we introduce the concepts of α,θ-admissible Banach contraction, α,θ-admissible crooked Banach contraction, and α,θ-admissible φ,β-contraction in an extended ϕ,ψ-metric space. We augment our theoretical results by providing compelling and nontrivial illustrative examples.
ISSN:2314-8896
2314-8888
DOI:10.1155/2024/7723630